§18.37(iii) OP’s Associated with Root Systems

Orthogonal polynomials associated with root systems are certain systems of
trigonometric polynomials in several variables, symmetric under a certain
finite group (Weyl group), and orthogonal on a torus. In one variable they are
essentially ultraspherical, Jacobi, continuous q-ultraspherical, or
Askey–Wilson polynomials. In several variables they occur, for q=1, as
Jack polynomials and also as Jacobi polynomials associated with
root systems; see Macdonald (1995, Chapter VI, §10),
Stanley (1989), Kuznetsov and Sahi (2006, Part 1),
Heckman (1991). For general q they occur as Macdonald
polynomials for root system An, as Macdonald polynomials for general
root systems, and as Macdonald-Koornwinder polynomials; see
Macdonald (1995, Chapter VI), Macdonald (2000, 2003), Koornwinder (1992).